Rewrite the function by completing the square. $f(x)=x^{2}-16x-100$ $f(x)=(x+$
Explanation: We want to complete $x^2{-16}x$ into a perfect square. To do that, we should add $\left(\dfrac{{-16}}{2}\right)^2={64}$ to it: $x^2{-16}x+{64}=(x-8)^2$ In order to keep the expression equivalent, we add and subtract ${64}$, not forgetting the expression's constant term, $-100$ : $\begin{aligned} f(x)&=x^2-16x-100 \\\\ &=x^2-16x+{64}-100-{64} \\\\ &=(x-8)^2-100-64 \\\\ &=(x-8)^2-164 \end{aligned}$ In conclusion, after completing the square, the function is written as $f(x)=(x - 8)^2 -164$ This is equivalent to $f(x)=(x+{-8})^2-164$